Sections 14.2, 15.1, 15.7 PRINCIPLES OF MECHANICS A force F(x,y,z) acts on a particle of mass m and moves it from point P(x ,y,z) at time t, to point P2(X2, Y2,22) at time t2 along curve C. The velocity of the particle is v, at P1 and v2 at P2- 1 2 ARC LENGTH S 12 TIME t P(x, y, z) P (x,3,4) TIME t, fc /10- 5, 15 12 CURVE C = F P (x, "?) TIME +2 ARE LENGTH $ 2 1- Dy ×
Sections 14.2, 15.1, 15.7 PRINCIPLE OF IMPULSE AND MOMENTUM m? + [ F dt = mv2 $1 PRINCIPLE OF IMPULSE OF TORQUE AND ANGULAR MOMENTUM ? ¡¡ ×m?+ f?xFdt = ?2×m?2 1 PRINCIPLE OF WORK AND ENERGY 1 2 1 2 J F . di = - mv -mv + 2 1 2 2 P1 + P2 : C
Section 15.7 Principle of Angular Impulse and Angular Momentum PRINCIPLE OF ANGULAR IMPULSE AND ANGULAR MOMENTUM · Principle of Angular Impulse and Angular Momentum: ! 02 where 1 MO =f!F That is, H =f !mv r and r ? r t1 t2 I ! mv + "f ! F dt= f, ! m V2 r. r H, is the angular momentum of the particle M, is the moment of the force F acting on the particle t2 r I Mo dt is the angular impulse on the particle The angular impulse is the impulse of the moment of the force F acting on the particle, that is, the impulse of the torque on the particle. · The Principle of Angular Impulse and Angular Momentum states that the impulse of the torque on the particle changes the particle's angular momentum.